Question

I’m pretty new at Matlab so would need a baby-steps explanation.

I have some MIDI data which looks a bit like this:

time on/off note
10 1 61
90 0 61
90 1 72
92 1 87
100 0 72

What I want to do is expand or ‘fill-in’ the gaps so that I have a row for every single moment in time, and I have columns which show which notes are on (there is often more than one note at the same time).

the ultimate goal is to do some calculations about the overall relationship between notes on (the harmonic dissonance) at a given time.

So I was thinking that maybe I needed a new column for every single possible note (there are 127), and then a 1 or 0 for every time. Or maybe I can just have a matrix which just tells me which notes are on (so the number of columns varies).

I wrote my own pseudo-code, but have no idea how to implement it. I suspect there is a simple function that can do this. Here is my pseudo-code:

start with 0, at time 0 in a new ‘notes-on matrix’
for numbers: 0 to n
if the number matches a number in the time column, go to the on/off column for that row.
if 1 in on/off column then copy number in notes column to ‘notes-on matrix’ for corresponding row
if 0 then don’t copy/do nothing.

if number doesn’t match number in time column
copy the previous row (which can be blank if there were no notes on).

for each row in the new ‘notes-on matrix’, arrange numbers low to high in different columns.

So can anyone tell me what to do?? I’m banging my head against a brick wall here!

Answer 1

Here’s a solution that will work even if the list is in a completely random order. It is based on the following idea: The cumulative sum of the vector [0 1 0 0 -1 0 0] is [0 1 1 1 0 0 0]. This corresponds to “on” in time 2, and “off” in time 5. Now all we need to do is populate an array with 1 and -1, and run CUMSUM to transform it into an array that has, in each column, ones whenever the sound is on.

I assume that there are 128 notes (0-127), and that you want to have one time step of silence (if all notes eventually end) at the very end. Note that Matlab starts counting at 1, so time 0 corresponds to row #1.

%# midiData is a n-by-3 array with [time,on/off,note]
midiData = [...
10 1 61
90 0 61
90 1 72
92 1 87
100 0 72];

%# do not call unique here, because repeated input rows are relevant

%# note values can be from 0 to 127
nNotes = 128;

%# nTimepoints: find the highest entry in midiData's time-column
%# add 2, because midiData starts counting time at 0
%# and since we want to have one additional timepoint in the end
nTimepoints = max(midiData(:,1))+2; 




%# -- new solution ---
%# because the input is a bit messed up, we have to use a more complicated
%# solution. We'll use `accumarray`, with which we sum up all the
%# entries for on (+1) and off (-1) for each row(time)/column(note) pair.
%# after that, we'll apply cumsum

%# transform the input, so that 'off' is -1
%# wherever the second col of midiData is 0
%# replace it with -1
midiData(midiData(:,2)==0,2) = -1;

%# create output in one step
%# for every same coordinate (time,note), sum all the 
%# on/offs (@sum). Force the output to be 
%# a nTimepoints-by-nNotes array, and fill in zeros
%# where there's no information
output = accumarray(midiData(:,[1 3])+1,midiData(:,2),...
    [nTimepoints,nNotes],@sum,0);

%# cumsum, and we're done
output = cumsum(output,1);

The previous solution, for completeness:

%# --- old solution ---

 %# create output array, which we'll first populate with 1 and -1
%# after which we transform it into an on-off array
%# rows are timepoints, columns are notes
output = zeros(nTimepoints,nNotes);

%# find all on's 
%# onIdx is 1 if the second column of midiData is 1
onIdx = midiData(:,2) == 1;

%# convert time,note pairs into linear indices for
%# writing into output in one step
%# Add 1 to time and note, respectively, so that we start counting at 1
plusOneIdx = sub2ind([nTimepoints,nNotes],midiData(onIdx,1)+1,midiData(onIdx,3)+1);

%# write "1" wherever a note turns on
output(plusOneIdx) = 1;

%# now do the same for -1
offIdx = midiData(:,2) == 0;
minusOneIdx = sub2ind([nTimepoints,nNotes],midiData(offIdx,1)+1,midiData(offIdx,3)+1);

%# instead of overwrite the value in output, subtract 1
%# so that time/note that are both on and off become zeros
output(minusOneIdx) = output(minusOneIdx) - 1;

%# run cumsum on the array to transform the +1/-1 into stretches of 1 and 0
%# the 'dim' argument is 1, because we want to sum in the direction in 
%# which rows are counted
output = cumsum(output,1);

%# for fun, visualize the result
%# there's white whenever a note is on
imshow(output)